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Background/Objectives: Neoadjuvant therapy (NAT) is now central to the management of borderline resectable (BRPC) and locally advanced (LAPC) pancreatic ductal adenocarcinoma (PDAC). This narrative review summarizes contemporary evidence and guidelines from a surgical perspective, with emphasis on pretreatment classification, post-NAT selection for exploration, intraoperative vascular strategy, and postoperative management. Methods: We conducted a structured narrative review of randomized and prospective studies, high-quality observational cohorts, and major international guidelines published through 31 July 2025. Results: BRPC and LAPC remain primarily defined by vascular anatomy, but biologic and conditional factors are increasingly integrated into decision-making. NAT is the preferred initial strategy for BRPC and the standard induction approach for LAPC, with resection considered only in carefully selected responders. After NAT, contrast-enhanced CT combined with CA19-9 kinetics remains the core restaging platform, while FDG-PET, diffusion-weighted MRI, radiomics, and circulating biomarkers may serve as adjuncts in equivocal cases. Surgical exploration should be guided by physiologic recovery, the absence of metastatic progression, and multidisciplinary reassessment. Staging laparoscopy remains useful for detecting occult metastatic disease. Intraoperatively, vascular resection should be margin-driven rather than routine, with portal–mesenteric venous resection established in expert centers, whereas arterial resection remains highly selective. Periarterial divestment represents an artery-sparing alternative in selected cases. NAT does not appear to worsen short-term postoperative outcomes, but anticoagulation after venous reconstruction remains non-standardized. Conclusions: NAT has transformed BRPC/LAPC PDAC into a biology-gated, time-sequenced surgical pathway. Standardized reassessment, careful candidate selection, and the centralization of complex vascular procedures are essential to optimize outcomes.